In recent years, topological dynamics have become an important tool in model theory. I will talk about some topological dynamical results from my PhD thesis about the so-called group-like equivalence relations. I plan to give a glimpse of the motivations in model theory (mostly related to the model-theoretic Galois groups and connected components of definable groups) and to show some ideas of the proofs.
I will briefly recall the required notions from topological dynamics. Some knowledge of model theory will help to understand the motivations, but otherwise, it will not be necessary.